The models with single absorbing configurations like directed percolation [1]}, [2]} and contact process [3]} have one open CC and one closed CC as in Fig. REF blue(b). Let \(w_{\mathcal {C}_i\rightarrow \mathcal {C}_j}\)  be the non-negative transition rate from configuration \(\mathcal {C}_i\)  to configuration \(\mathcal {C}_j\)  and the configuration \(\mathcal {C}_0\)  corresponds to absorbing configuration. The \(n\)th component of the column vector \(|P(t)\rangle \)  is the probability that system in configuration \(\mathcal {C}_n\)  at time \(t\) . The Master equation for the dynamics is
\(\frac{\mathrm {d}}{\mathrm {d} t}|P(t)\rangle = \mathbf {M}|P(t)\rangle ,\quad \mathrm {where}~{\bf M}=\begin{pmatrix}0 & \langle w|\\\mathbf {0} & {\bf A}\\\end{pmatrix}, \) 
